The Moore-Penrose and group inverse of square matrices and the Jordan canonical form

Abstract

This paper is a continuation of the paper [3], where the first two Penrose's equations are solved for a square matrix, which is transformed into the Jordan canonical form. Our main aim is to solve the other two Penrose's equations for the same class of matrices. We also find a block representation of the group inverse and the form of the corresponding Jordan matrix, by solving the corresponding set of equations.